Yep, I agree. Orange HRM is the best solution for you. It works hassle-free and installs seamlessly. I know a company that provides a hosted solution for Orange; you can use that if you do not have a server in the office. Since your employees are pan India, a hosted solution will make more sense. Otherwise, you need a server in the office that is accessible for people from outside as well. Not sure if your office allows that.
Considerations for Orange HRM
Also, note that it does not have a payroll solution (most HRMS solutions don't have payroll). Additionally, the software is free as it is open source. But if you need help from experts to implement it, then you need to pay for it.